LAUSR

This paper presents a novel approach to state-feedback stabilization of polynomial systems with bounded actuators. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the Lyapunov matrices. Therefore, parameterization of the state-feedback controllers is independent of the Lyapunov matrices. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition is cast as convex optimization using the sum-of-squares technique and can be efficiently solved. In addition, the novel parameter-dependent Lyapunov functions are readily applied to robust state-feedback stabilization of polynomial systems subject to parametric uncertainty. Effectiveness of the proposed approach is demonstrated by numerical examples.